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Universal series induced by approximate identities and some relevant applications.
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2011-06-12 , DOI: 10.1016/j.jat.2011.06.001 Vassili Nestoridis 1 , Sebastian Schmutzhard 2 , Vangelis Stefanopoulos 3
中文翻译:
由近似恒等式和一些相关应用引起的通用级数。
更新日期:2011-06-12
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2011-06-12 , DOI: 10.1016/j.jat.2011.06.001 Vassili Nestoridis 1 , Sebastian Schmutzhard 2 , Vangelis Stefanopoulos 3
Affiliation
We prove the existence of series , whose coefficients are in and whose terms are translates by rational vectors in of a family of approximations to the identity, having the property that the partial sums are dense in various spaces of functions such as Wiener’s algebra , , , , for every , and the space of measurable functions. Applying this theory to particular situations, we establish approximations by such series to solutions of the heat and Laplace equations as well as to probability density functions.
中文翻译:
由近似恒等式和一些相关应用引起的通用级数。
我们证明系列的存在 ,其系数 在 以及谁的条款 由有理向量翻译 恒等式的一个近似族,具有以下性质:部分和在诸如维纳代数的各种函数空间中是密集的 , , , ,每个 ,以及可测量功能的空间。将此理论应用于特定情况,我们通过此类级数建立热和拉普拉斯方程解以及概率密度函数的近似值。